A body of mass 2 kg moves under a force of ( 2î + 3ĵ + 5k̂ )N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is _____________. (Round off to the Nearest Integer)

Solution

Physics sir · 4 steps

Force is constant, so treat each axis on its own: find the acceleration, then use s = 1/2at².

1. Find acceleration. Divide the force by the mass: a⃗ = F⃗/m = (2î + 3ĵ + 5k̂)/2 = î + 1.5ĵ + 2.5k̂ m s⁻². The force is constant, so this acceleration is constant too.
2. Displacement from rest. The body starts from rest at the origin, so along every axis the coordinate after time t is just the displacement.

   r⃗ = 1/2a⃗ t² = 1/2a⃗ × 16 = 8 a⃗

3. Check each axis. x = 8 × 1 = 8 and z = 8 × 2.5 = 20, which match the given coordinates. Along y, b = 8 × 1.5 = 12.
4. So. The y-coordinate after 4 s is b = 12 m, so the answer is 12.

The common slip: 24. Dropping the 1/2 in s = 1/2at² gives 1.5 × 16 = 24, not 12. Check the x-coordinate: it would come out as 16 instead of the given 8.

The idea to keep. A constant force vector means constant acceleration along each axis separately. Split it into components and apply the one-dimensional kinematics equations to each.

Answer from the NTA final answer key. Solution by PrepWiser.